A180343 a(0)=-4; a(n+1) = 2*a(n) + period 4: repeat 6,1,2,5.

-4, -2, -3, -4, -3, 0, 1, 4, 13, 32, 65, 132, 269, 544, 1089, 2180, 4365, 8736, 17473, 34948, 69901, 139808, 279617, 559236, 1118477, 2236960, 4473921, 8947844, 17895693, 35791392, 71582785, 143165572, 286331149, 572662304, 1145324609, 2290649220, 4581298445

Offset: 0

Author

Paul Curtz, Jan 18 2011

Keywords

• sign
• easy
• less

Comments

Period 4:repeat 6,1,2,5 = A131800(n-1).

Examples

			a(1) = 2*(-4) + 6 = -2;
a(2) = 2*(-2) + 1 = -3;
a(3) = 2*(-3) + 2 = -4;
a(4) = 2*(-4) + 5 = -3;
a(5) = 2*(-3) + 6 =  0.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,1,-2).

Programs

Magma

I:=[-4, -2, -3, -4, -3]; [n le 5 select I[n] else 2*Self(n-1)+Self(n-4)-2*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

Maple

A112030 := proc(n) (2+(-1)^n)*(-1)^floor(n/2) ; end proc:
A180343 := proc(n) -2/5*A112030(n+1)-(-1)^n/6-7/2+2^n/15 ; end proc: # R. J. Mathar, Jan 18 2011

Mathematica

CoefficientList[Series[(-4+6*x+x^2+2*x^3+9*x^4)/((x-1)*(2*x-1)*(1+x)*(x^2+1)),{x,0,40}],x] (* Vincenzo Librandi, Jun 17 2012 *)
LinearRecurrence[{2,0,0,1,-2},{-4,-2,-3,-4,-3},40] (* Harvey P. Dale, Sep 06 2020 *)

Formula

G.f.: ( -4 + 6*x + x^2 + 2*x^3 + 9*x^4 ) / ( (x-1)*(2*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Jan 18 2011

a(n) = 2*a(n-1) + A131800(n+2).

a(n) = a(n-4) + 2^n.

a(n) = a(n-2) + 4*A007909(n) (A007909(0)=0). From second -3.

a(n) = -2*A112030(n+1)/5 - (-1)^n/6 - 7/2 + 2^n/15. - R. J. Mathar, Jan 18 2011

a(n) = 2*a(n-1) + a(n-4) - 2*a(n-5). - Vincenzo Librandi, Jun 17 2012